The focal lengths of a convex lens for blue and red colors of light are `f_(B)` and `f_(R )` respectively, and those of a concave lens are `f'_(B)` and `f'_(R )` then

Options

A. `f_(B)gtf_(R )` and `f'_(B)ltf'_(R )`
B. `f_(B)ltf_(R )` and `f'_(B)gtf'_(R )`
C. `f_(B)gtf_(R )` and `f'_(B)gtf'_(R )`
D. `f_(B)ltf_(R )` and `f'_(B)ltf'_(R )`

Answer

To solve the problem regarding the focal lengths of a convex lens for blue and red colors of light, and those of a concave lens, we need to understand the concept of chromatic aberration and how different wavelengths of light behave when passing through lenses.

### Step-by-Step Solution:

1. **Understanding Focal Lengths**:
- The focal length of a lens depends on the wavelength of light passing through it. Generally, shorter wavelengths (like blue light) will have a shorter focal length compared to longer wavelengths (like red light) when passing through a lens.

2. **Convex Lens Focal Lengths**:
- For a convex lens, the focal length for blue light (`f_B`) is shorter than that for red light (`f_R`):
\[ f_B < f_R \]

3. **Concave Lens Focal Lengths**:
- For a concave lens, the situation is similar but inverted. The focal length for blue light (`f'_B`) will be longer (less negative) than that for red light (`f'_R`):
\[ f'_B > f'_R \]

4. **Conclusion**:
- Therefore, we can summarize the relationships as follows:
- For a convex lens: \( f_B < f_R \)
- For a concave lens: \( f'_B > f'_R \)

5. **Final Statement**:
- The focal lengths of the lenses vary with the color of light due to the difference in wavelengths, leading to different degrees of refraction.